Results are presented on an alternative cavity to the ILC baseline design of TESLA-style SRF main accelerating linacs. This re-optimised shape enhances the bandwidth of the accelerating mode and has reduced surface electric and magnetic fields, compared to the baseline design and some current high gradient designs. Detailed simulations on the e.m. fields for the New Low Surface Field (NLSF) cavity, including end-cell and coupler designs, are reported. The re-distributed dipole modes are also discussed